You hear it in the dingy corners of a crumbling Westminster Palace, at discreetly expensive restaurants and in noxious, Christmas-festooned pubs. You hear it from former prime ministers and lowly special advisers, and even from foreign leaders.

“Brexit will not happen.” It cannot actually happen. Parliament, we are told, will force the deluded people to come to their senses, aided by the judiciary and big business. If the people have made a mistake, then can they not be shown the latest economic forecasts and be obliged, somehow, to think again?

With respect to all involved, and – briefly – to adopt the demotic of Boris Johnson, this must be cobblers. If parliament asked the people of the UK to vote on a subject of such huge importance; and if, after exhaustive and exhausting debate, they made their decision, by a clear majority; and if they were then told that it wasn’t going to happen, or at least not without a second vote, the glossy fabric of British democracy would be ripped to shreds. Frankly, I dread to think what would follow.

It is time to think differently. Brexit is coming, and relatively soon. We have to assume that the UK will be outside the EU within two and a bit years. An entirely new chapter in our politics will then begin. Yet most of the British political class is so battered and demoralised by the Brexit decision that they cannot take what is likely at face value, and start to chart how they intend to reshape a country that has much more power over its own governance.

This is odd; and it is a dangerous wasted opportunity. Parliamentary power, expan­ded and reinforced, gives new opportunities to both the left and the right to change Britain. Rather than being paralysed by fear, we ought to be on the lip of a great invigoration of our democracy. Yet hardly anyone seems to be talking about the new agendas that are opening up.

On the left, this may reflect a terror that leaving the EU will inevitably result in a slaughter of regulations and a Hobbesian global-trade state, in which workers’ rights and environmental protection will go by the board. On the right, the lack of imagination about what, after all, so many people have been campaigning for, and for so long, is stranger still. It mostly adds up to a vague feeling that there will be less “meddling” and that the pungent odours of the 1950s – coal-smoke, hand-knitted woollen jumpers, bleach – will magically reappear.

Yet we are not going to be a different people. The instincts of the British electorate haven’t suddenly changed during 2016. It’s unlikely that we will veer enthusiastically back to the distant pre-European-migration past, or cast aside liberal and environmental ways of thinking that have become valuable to us in recent decades. For left and right alike, this is going to be a time of fresh, vivid and urgent debate.

We have to start, of course, with trade. Through the thick miasma of official waffling, some things are already becoming clearer. We will be out of the single market and will be out of a customs union – because if we weren’t, we wouldn’t be able to negotiate our own trade agreements around the world. Theresa May would hardly have created a new Department for International Trade if she intended it to have no purpose.

Yet the pressure from business and industry for access to European markets is also such that her government is going to have to offer Europe a deal on the movement of workers. The logical conclusion is that we will see sector-by-sector agreements to allow in X thousand electricians, or Y thousand careworkers, with industry bodies given coupons by the government and allowed to issue the work visas they require. This is the kind of thing that might allow EU leaders to grant low-tariff or tariff-free access to some markets, and stave off a downward economic lurch.

What it will also involve, obviously, is a higher level of continued movement from the EU into the UK than many Brexit voters expect. But the government will honourably be able to claim that it has “taken back control”. It will allocate the numbers coming in, giving it more direct influence on business and industry generally. As was hinted at with the early deal with Nissan, the change could prompt a move towards more physical manufacturing, at the expense of the service sector.

This is something politicians have been talking about since the 1970s, from Harold Wilson to George Osborne, to relatively little effect. After the deindustrialisation and Big Bang of the Thatcher/Geoffrey Howe era, our economy has drifted steadily further into financial services. We have been arguing, increasingly bitterly, about some of the consequences: the huge rewards for a small minority of bankers; the lack of German-style support for industrial manufacturing and the consequent lack of jobs for people who want to work with their hands; and the increasing imbalance in wealth and power between the metropolis and the Midlands.

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Some of the measures the left would like to take to support and protect the steel industry, or engineering, or to enhance our growing advantage in robotics, are made impossible not by British Conservatives, but by EU regulations on competitiveness and state funding. Make no mistake: an awful lot is back in play. Rail renationalisation, for one, despite the announcement this month about franchising of train tracks.

It is true that a Brexit deal that secured the interests of British carmakers while failing to secure the City’s “passporting rights” – so leading to a haemorrhage of financial institutions to Frankfurt, Dublin or Paris – would be extremely painful for the Treasury and the British state. Indeed, whether or not Brexit can be made to work financially will depend to a large extent on our ability to strike an early UK-US trade agreement that allows Britain to sell its service sector into the American market. Otherwise, the loss of tax revenues would be something the rest of us would have to make up, and austerity would be extended to cover a screeching handbrake-turn for the economy. Philip Hammond’s pallor is scary enough as it is, thank you very much.

Looking further ahead, however, manufacturing is already being transformed with new materials and 3D printing; there is no longer any reason to assume an endless downward spiral. The prospect of a new industrial policy is, in a sense, being forced upon Britain by the Brexit vote, but that is good news, not bad news: it ought to produce the most vigorous and excited debate.

Shrewder politicians on the left and right are already thinking about the opportunities raised by new trade agreements. Leading Tories see deals with poorer countries leading to cheaper clothing and food imports than we have now. Many EU trade deals with developing countries don’t include services because they don’t matter so much to other EU member states; they can now be extended to benefit us.

On the other side of the fence, Labour’s Brexit committee has been looking at how the left might develop a critique of global­ism. Part of this could involve the trade treaties to come so that they include environmental and worker protection clauses (and, indeed, human rights provisions) alongside agreements on tariffs.

Those involved, such as John McDonnell and Barry Gardiner, are discussing how a future Labour government could use British corporate expertise to leverage deals that are both progressive and expand trade. The Scotch whisky industry wants lower tariffs for the Indian market, for instance, but also boasts immense expertise on water quality, a big issue for Narendra Modi’s government. Are there more creative and imaginative agreements to be struck between Britain and India post-Brexit?

Defence is another significant area that will change. We remain, of course, in Nato and we should stop trying to hector the remaining EU countries about their own defence arrangements. But with Donald Trump in the White House, Nato will feel very different and with Putin’s Russia pushing hard, an independent UK will need to think about defence afresh. Now that even senior members of the defence establishment privately accept that Trident is old technology and increasingly vulnerable to satellites and drones, we ought to be having a big debate about what kind of defence we need and where our deeper interests lie (Estonia? Turkey?). What once was unthinkable no longer is.

Given that Britain, with GCHQ, is already a world leader in cyber security, we may well decide to ditch nuclear submarines in favour of a vast increase in intelligence. It is very unlikely, as the world gets more dangerous, that we will be able to spend less on defence. There won’t be a “No to nukes, Yes to better childcare” option of the kind the left would feel comfortable with. Our armed forces won’t be cheap but they will be very different; and yet politicians have so far said almost nothing about this. We have had a deep-frozen defence debate for years; it’s time for that to change.

The same kind of profound changes will be available in foreign policy. Able to act independently, Britain can forge a different policy for the Middle East; we can make our own policy on human rights in China, too. After Brexit, we should see a return to something like health for the ignored and enfeebled Foreign Office.

All of this, however, is only the beginning. The range of domestic policies that can now be thoroughly altered is breathtaking, covering everything from the funding of schools to forestry to employment rights. One area with scope for change is agriculture, which has been deeply enmeshed in EU lawmaking policy covering everything from the size of hedgerows and gates to inspection regimes for various kinds of farm, all tied to the doling out of subsidies from urban voters. Whatever version of Brexit is finally agreed, it seems inconceivable that farmers won’t want the best possible access to European markets for their meat, cereals and even wine. Consequently, any new inspection and hygiene regime will have to be at least as good (and therefore as intrusive) as the one we have now.

There are many other possibilities, though not all farmers will be pleased to hear about them. A different subsidy regime could tilt away from the largest landowners, who are already wealthy, to give extra support to struggling family farms and hill farmers – the kind the urban public most often admires and supports. (Cue howls of outrage from the Lords.)

We could have new laws to encourage the replanting of hedgerows and coppices, to protect our endangered birdlife. Some interesting work on forestry futures has been done by the government’s natural capital committee. Across the UK, only 6 per cent of our economy is low-carbon, but that has produced 30 per cent of growth over the past three years. Our island ecosystem is European but also subtly different, and we can handcraft legislation to reflect that.

Or, if we choose to accept that we are now an essentially urban country, a future government could tear up restrictions on housebuilding and urban sprawl and give the green light for widespread planting of genetically modified crops. At its most extreme, it could stop subsidising farming altogether, arguing that we already import most of our food, and that limited countryside space may be needed more for housing and recreation. Whether you think that’s a clever idea, or likely to lead to hideous shredding of communities, at least it’s a choice that will soon become available.

Environmental policy could be another area of change, though we are highly unlikely to follow Donald Trump’s lead and ditch all our green commitments. The big choices on energy policy will be the same outside the EU as inside: carbon emissions are now dealt with by a global treaty. Post-Brexit, are we going to opt for a somewhat less secure or safe nuclear industry? I rather doubt it.

In practice, we are becoming a more environmentally sensitive culture. It is hard to see a future government loosening laws on restricting airborne pollution from industrial plants, or on the disposal of chemical and electrical goods. Even the most right-wing Conservative administration is unlikely to make it easier to open new landfill sites or dispose of chemicals into rivers or near beaches.

Are we likely to want to reverse the effects of the EU’s Birds Directive? On the contrary, after Brexit, I would expect great British organisations such as the RSPB and the National Trust to become bigger voices in the national debate. In most of these areas, the freedom for manoeuvre will enable us to bring in better and tighter regulations, based on the needs of our own wildlife and landscape. At the very least, we can now look forward to arguments about pollution, waste and the proper protection of the landscape becoming fiercer than ever.

Coastal communities could be transformed by our leaving the EU. Old fishing towns have lost out to the growth in big corporate fleets, often owned by non-British companies, scooping up and processing the fish offshore. Gutting, smoking and the rest of preparation is no longer done around the ports and much of the “under ten” (smaller boats less than ten metres long) has vanished. All of this can be reversed.

Much of the EU regulation on fishing is designed to prevent overfishing and to protect stocks from spread of disease, particularly on fish farms. So unless we decided to overfish our own waters brutally, a quickly self-defeating policy – or unless we don’t care about exporting seafood – the space for expansion would seem limited. We could, however, go in entirely the other direction and introduce more stringent safety and hygiene rules, so that our exports would be particularly valued. Thinking bigger, there is now nothing to stop us creating our own extensive undersea conservation areas. Environmentalists are worried about the effects of bottom trawling on the North Sea. We could fish less, not more.

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On the other side of the world, the New Zealand government is creating the Kermadec underwater conservation park, a thousand kilometres north-east from the country’s shores. It will be an enormous area where all fishing as well as oil and gas exploration will be banned. New Zealand has shown that by putting “Keep Out” signs on significant parts of the ocean, it can even replenish fish stocks and biodiversity faster than scientists once thought possible. Could we do the same up here? The North Atlantic is a very different environment from the North Pacific, but a future British government could take a more assertive approach to underwater conservation. Whether or not it pleases pro-Brexit fishermen, it could prove a far-sighted environmental policy.

Those are just a few thoughts. There are probably many other areas where we will see a revived policy debate. Once we have control over VAT rates, and indeed the ability to create our own purchase tax, we can do away with absurdities such as taxes on tampons, and craft a tax system to encourage and discourage different kinds of spending – say, differential rates for high-sugar products, or special tariffs on electronic products that are hard to recycle. Why not?

There’s going to be a vigorous argument about all of that. But that is exactly my point. Almost without notice or comment, British politics has developed its own dependency culture, losing self-confidence about important changes of direction. Because of “Brussels”, politicians and civil servants have become a bit “computer says no”, taking it as the first principle that we can’t do this, we can’t do that. We can’t protect industries. We can’t really change economic direction. We can’t create new industrial hubs. We can’t change policy for the countryside. Well, now we can.

The defeated centre has spent a lot of time since the referendum asking whether the Great Disaster was “really” all about ingrained racism, fear of the modern world or media manipulation. Wouldn’t it be healthier to decide that the Leave side’s victory was about what it said on the tin – reclaiming political control – and then ask ourselves what we can now do with that extra freedom?

For all of us who believe in British democratic culture, there can be exciting times ahead. The winds of change can be invigorating, not simply bloody cold.

Andrew Marr is a broadcaster and journalist. Formerly the BBC’s Political Editor, he presents the Andrew Marr Show on BBC1 on Sundays and Start the Week on Monday mornings on Radio 4.